Problem: Simplify the following expression: $z = \dfrac{10}{9y} + \dfrac{1}{8y}$
In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $9y$ and $8y$ $\lcm(9y, 8y) = 72y$ $ z = \dfrac{8}{8} \cdot \dfrac{10}{9y} + \dfrac{9}{9} \cdot \dfrac{1}{8y} $ $z = \dfrac{80}{72y} + \dfrac{9}{72y}$ $z = \dfrac{80 +9}{72y}$ $z = \dfrac{89}{72y}$